will mark brainliest. PROMISE!! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
Compute the flux of the vector field LaTeX: \vec{F}=F → =< y + z , x + z , x + y > though the unit cubed centered at origin.
Assuming the cube is closed, you can use the divergence theorem:
[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]
where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].
We have
[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]
so the flux is 0.
A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot? ft (smaller value) by ft (larger value)
Answer:
50ft by 120ft
Step-by-step explanation:
Area of a rectangle = L × W
6000ft² = L × W
L = 6000/W
When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.
The formula for a right angle triangle =
a² + b² = c²( c = hypotenuse)
We are told in the question that:
A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel
Let us assume the side that the hypotenuse is longer than = Width
Hence, the Diagonal = (W + 10)²
Therefore
L² + W² = (W + 10)²
Since L = 6000/W
W² + (6000/W)² = (W + 10)²
W² + (6000/W)² = (W + 10) (W + 10)
W² + (6000/W)² = W² + 10W + 10W + 100
W² + (6000/W)² = W² + 20W + 100
W² - W² + (6000/W)² = 20W+ 100
6000²/W² = 20W + 100
6000² = W²( 20W + 100)
6000² = 20W³ + 100W²
20W³ + 100W² - 6000² = 0
20W³ + 100W² - 36000000 = 0
20(W³ + 5W² - 1800000) = 0
Factorising the quadratic equation,
20(W − 120)(W² + 125W + 15000) = 0
W - 120 = 0
W = 120
Therefore,
W(Width) = 120feet
Since the Width = 120 feet
We can find the length
6000ft² = L × W
L = 6000/W
L = 6000/120
L = 50 feet
The dimensions of the land, correct to the nearest foot is 50ft by 120ft
The data given below consists of the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12. Find the z-score corresponding to the median of school allergies. You may use your calculator to find the mean and standard deviation.
Answer:
z -score = 0.0459
Step-by-step explanation:
Given that:
the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.
The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.
Mean = sum of the sample/ total number of the sample
Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25
Mean = 219/25
Mean = 8.76
Standard deviation = [tex]\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}[/tex]
Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)
Standard deviation = [tex]\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }[/tex]
Standard deviation = 5.2174
The standard z score formula is:
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
where X = median (13th observation ) = 9
[tex]z = \dfrac{9- 8.76}{5.2174}[/tex]
[tex]z = \dfrac{0.24}{5.2174}[/tex]
z -score = 0.0459
Select the best with the least expensive corn per ounce The choices are in the image
Answer:
B
Step-by-step explanation:
Option A:
1.50÷18≈0.0833
3.00÷36≈0.0833
4.50÷54≈0.0833
Option B:
0.75÷15=0.05
Option C:
2.20÷15=0.146
Joes bait shop brought in a gross profit in sales of $4,100.00 in the month of June. During the same month their operating expenses totaled $1990.00. Calculate the net income of the bait shop for the month of June
Answer:
2110
Step-by-step explanation:
4100-1990=2110
Stock prices used to be quoted using eighths of a dollar. Find the total price of the transaction. 400 shares of national semi at 135 1/2
Answer:
The value is [tex]T = \$54200[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares is n = 400
The rate of each share is [tex]k = 135\frac{1}{2} = 135.5[/tex]
Generally the total price is mathematically represented as
[tex]T = 400 * 135.5[/tex]
[tex]T = \$54200[/tex]
For f(x) = 3х – 5 and g(x) = х2+ 2, find (f+ g)(x).
ОА. ? + 3х – 7
ОВ. 3х2 – 30
Ос. 3х3 – 3
OD. х2 + 3х - з
Answer:
x^2 +3x -3
Step-by-step explanation:
f(x) = 3х – 5
g(x) = х^2+ 2,
(f+g)(x) = 3х – 5 +х^2+ 2
Combine like terms
= x^2 +3x -3
Answer the question that follow about the given sequence. “Does not exist” and “none” are valid answers. Blank answers will be counted incorrect. -33, -27, -21, -15, … a. Arithmetic/Geometric/Neither? b. State the Common Ratio or Common Difference. c. Find the explicit formula for the nth term d. Find the recursive formula for the nth term e. Value of the 10th term f. ∑ notation for the Infinite Series. g. Sum of the Infinite Series.
Answer:
it's an arithmetic sequence with common difference 6An=6n-39, A10=21Sn=3n'2-(39/2)n88%
19. What is the solution X in this equation? 2(3x - 7) + 4(3x + 2) = 6(5x+9) + 3
[tex]\\ \sf\longmapsto 2(3x-7)+4(3x+2)=6(5x+9)+3[/tex]
[tex]\\ \sf\longmapsto 6x-14+12x+8=30x+54+3[/tex]
[tex]\\ \sf\longmapsto 6x+12x-14+8=30x+57[/tex]
[tex]\\ \sf\longmapsto 18x+6=30x+57[/tex]
[tex]\\ \sf\longmapsto 30x-18x=6-57[/tex]
[tex]\\ \sf\longmapsto 12x=51[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{51}{12}[/tex]
Simplify . 7+ the square root of 6(3+4)-2+9-3*2^2 The solution is
Answer:
7+sqrt(37)
Step-by-step explanation:
7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)
The quotient of 3 and the cube
of y+2
Answer:
[tex]\dfrac{3}{(y+2)^3}[/tex]
Step-by-step explanation:
Maybe you want this written using math symbols. It will be ...
[tex]\boxed{\dfrac{3}{(y+2)^3}}[/tex]
i need help thank u so much in advance !
Answer:
Questions .(1) 2/m. (2). m-1 . (3) 2 . (4) m
Answer:
(2m²-4m)/2(m-2)=2m(m-2)/2(m-2)= m
the answer is mm²-2m+1/m-1 ⇒ (factorize the nominator)(m-1)(m-1)/m-1 ⇒ ( m-1/m-1)=1
then answer is m-1(m²-3m+2)/(m²-m)=the answer is (m-2)/mm²-m-2/m²-1=(m-2)(m+1)/(m-1)(m+1)=the answer is m-2/m-1Which expression is equivalent to 2(5)^4
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
How many petals are on the graph? Find the trigonometric form of a given function.
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
Find the union and interesection of each of the following A={3,6,9,12}, B ={6,8,9}
Answer:
Hello,
The answer would be,
A union B = {3,6,9,12}
and A intersection B= {6,9}
Answer:
[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]
[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]
Step-by-step explanation:
A = {3,6,9,12}
B = {6,8,9}
A∪B = {3,6,9,12} ∪ { 6,8,9} [Union means all of the elements should be included in the set of A∪B]
=> A∪B = {3,6,8,9,12}
Now,
A∩B = {3,6,9,12} ∩ {6,8,9} [Intersection means common elements of the set]
=> A∩B = {6,9}
what is the magnitude of the vector?
Answer:
[tex]\boxed{\sqrt{65}}[/tex]
Step-by-step explanation:
Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]
Therefore, just plug in your x and y-values and solve.
[tex]\sqrt{4^{2}+7{^{2}}[/tex]
[tex]\sqrt{16 + 49}[/tex]
[tex]\sqrt{65}[/tex]
Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.
Use the equation p=6k+12 to find the value of p when k=9.
Answer:
66
Step-by-step explanation:
when you plug in 9 for k. you do 6(9) which is 54. then add 12 to 54 and thats ur answer, 66.
if 75% think the action is morally wrong, and we say there are 249 million adults in the country, how many believe that the action is morally wrong?
Answer: 186.75 million which is the same as saying 186,750,000
Work Shown:
75% = 75/100 = 0.75
75% of 249 million = 0.75*249 million = 186.75 million
186.75 million = 186.75*10^6 = 186,750,000
Answer:
186,750,000
Step-by-step explanation:
Take 75% of 249 million
.75 * 249,000,000
186,750,000
Identify the recursive formula for the sequence given by the explicit formula f(n) = 20 – 4(n − 1).
Answer:
[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Step-by-step explanation:
[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Answer:
Step-by-step explanation:
someone answered already
Find the total area the regular pyramid. T.A=
Answer:
18√91 +54√3
Step-by-step explanation:
Name the point at the top of the pyramid "A", the point at the left front corner "B", and the one in the center of the hexagonal base "C". Then right triangle ABC is shown. The "base" BC of that triangle is the same measure as the front edge (6), because the diameter of a regular hexagon is equal to twice the side length.
Using the Pythagorean theorem, we can find the face edge length to be ...
AB^2 = BC^2 +AC^2
AB^2 = 6^2 +8^2 = 100
AB = √100 = 10
If we call the midpoint of the front edge "D", then we need to find the length of AD in order to determine the face area. Again, we can use the Pythagorean theorem.
AB^2 = BD^2 +AD^2
AD^2 = AB^2 -BD^2 = 10^2 -3^2 = 91
AD = √91
The area of one of the 6 lateral faces is ...
A = (1/2)bh = (1/2)(6)√91 = 3√91
The area of one of the 6 equilateral triangles that make up the base is ...
A = (√3)/4·s^2 = (√3)/4(6^2) = 9√3
Then the total area of the pyramid is ...
total area = 6 × (face area + partial base area)
= 6(3√91 +9√3)
total area = 18√91 +54√3
Please help
Simple geometry / trig problem
Answer:
b, c, dStep-by-step explanation:
a. tan 30/ sin 30 = (sin 30/cos 30) / sin 30 = 1 / cos 30, no
b. cos 30 = √3/2, yes
c. cos 60 tan 60 = cos 60 (sin 60/cos 60) = sin 60 = cos 30, yes
d. sin 60 = cos (90 - 60) = cos 30, yes
[tex]\bf{b.}\ \ \it cos30^o=\dfrac{\sqrt3}{2}\ \ (True)\\ \\ \bf{d.}\ \ \it sin60^o=cos(90^o-60^o)=cos30^o\ \ (True) \\ \\ \bf{c.}\ \it cos60^o\cdot tan60^o=cos60^o\cdot\dfrac{sin60^o}{cos60^o}=\dfrac{cos60^o}{cos60^o}\cdot sin60^o=1\cdot sin60^o=cos30^o\ (T)\\ \\ \\ \bf{a.}\ \ \it \dfrac{tan30^o}{sin30^o}=tan30^o\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{cos30^o}\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{sin30^o}\cdot\dfrac{1}{cos30^o}=\\ \\ \\ =1\cdot\dfrac{1}{cos30^o}=\dfrac{1}{cos30^o}\ \ne\ cos30^o[/tex]
HELP ME!
A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?
Answer: approx 1196 students.
Step-by-step explanation:
As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)
2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.
95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392
Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.
N=2392:2=1196
PLS HELP :Find all the missing elements:
Answer:
[tex]\large \boxed{\mathrm{34.2}}[/tex]
Step-by-step explanation:
[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]
[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]
[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]
What is the missing digit?
820,107
– 65□,084
167,023
What is the mean of this data set?
A. 84
B. 85
C. 83
D. 88
Answer:
85
Step-by-step explanation:
Add to get total. divide by 4.
Answer:
B. 85
Step-by-step explanation:
Sorry for this very late response. But if anyone wasn't sure if 85 is the correct answer, it is. I can confirm this because I just took the test. I hope I could help! (:
you start at (5,3) you move down 4 units and up 6 units. where do you end?
You end up at the point (5, 5).
how many pieces each 31/6 metres long can be cut fram a cloth 155/2 metres long ?
Answer:
?
Step-by-step explanation
my 4th person to ask a question
Find the missing side lengths.
Answer:
x is 18, and y is 9 √ 3
Step-by-step explanation:
Since this is a right triangle that contains a 30 degree angle, we know this is a special right triangle, and the missing angle is 60 degrees since a triangle is 180 degrees, and 180 - 90 - 30 = 60.
The relationship is listed below:
The side opposite of the 30 degrees can be represented as a variable, say "p", and the hypotenuse which is x in your question is twice this. The side opposite of the 60 degree angle is x + √3
So x is 18, and y is 9√3
In empty set, n (A) = ………
Answer:
answer is
In empty set, n(A) = { }.